Lecture 2.2 | Part 1: Derivative rules.

Derivatives of Trigonometric functions

Lecture 2.2 | Part 3: Derivative rules.

• Composite functions.
• Introduction to the Chain rule.

Lecture 3.1: Differentiation rules.

• The chain rule.
• Examples of the Chain Rule.

Lecture 4.1: Max & Min Values

• Maximum & minimum values.
• Global & local maximum (minimum)

Lecture 4.2: Shapes of graphs

• Determining Increasing / decreasing regions
• Determining the concavity of graphs
• Inflection points

Lecture 6.1 | Part 1: Shapes of Graphs

• Examples of Increasing & Decreasing regions
• Examples of Local maximum & minimum
• Examples of Concavity regions

Lecture 6.1 | Part 2: Introduction to integration

• Antiderivatives
• Riemann Sum
• Definite integral

Lecture 6.2 | Part 1 | Quiz solution

• Optimization problem
• Local max/min using the first derivative test
• Local max/min using the second derivatives

Lecture 6.2 | Part 2 | Fundamental Theorems

• Fundamental theorem of calculus 1
• Fundamental theorem of calculus 2
• Newton-Leibnitz theorem

Lecture 7.1 | Intro to Areas using integrals

• Integration is the Net Area

Lecture 7.2 | Finding the areas using integrals

• Areas between the curves

Problem | Finding the areas between the curves

• Splitting the area into vertical rectangles
• Splitting the area into horizontal rectangles

Lecture 8.1 | Volumes using definite integrals

Mid-term Review | Part 1 | Differentiation

Mid-term Review | Part 2 | Integration

Lecture 10: Integration techniques

• Substitution rule
• Trigonometric integration
• Integration by parts
• Integration of rational functions
• Integration of radicals

Lecture 11.1: Average value. Arc length.

• Average value of a function
• Mean value theorem
• Finding the Length of curves

Lecture 11.2: Surface Area of Revolution.

• Surface areas of cylinders, cones
• Approximation of the surface area with bands
• Example: surface area of a sphere